Rocket nozzles: 75 years of research and development

Rocket nozzles: 75 years of research and development

SHIVANG KHARE1 and UJJWAL K SAHA2,*

1Department of Energy and Process Engineering, Norwegian University of Science and Technology,

7491 Trondheim, Norway2Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati 781039, India

e-mail: [email protected]; [email protected]

MS received 28 August 2020; revised 20 December 2020; accepted 28 January 2021

Abstract. The nozzle forms a large segment of the rocket engine structure, and as a whole, the performance of

a rocket largely depends upon its aerodynamic design. The principal parameters in this context are the shape of

the nozzle contour and the nozzle area expansion ratio. A careful shaping of the nozzle contour can lead to a

high gain in its performance. As a consequence of intensive research, the design and the shape of rocket nozzles

have undergone a series of development over the last several decades. The notable among them are conical, bell,

plug, expansion-deflection and dual bell nozzles, besides the recently developed multi nozzle grid. However, to

the best of authors’ knowledge, no article has reviewed the entire group of nozzles in a systematic and

comprehensive manner. This paper aims to review and bring all such development in one single frame. The

article mainly focuses on the aerodynamic aspects of all the rocket nozzles developed till date and summarizes

the major findings covering their design, development, utilization, benefits and limitations. At the end, the future

possibilities of development are also recommended.

Keywords. Rocket nozzle; aerodynamics; thrust; expansion ratio; nozzle contour; shock wave; method of

characteristics; efficiency.

1. Introduction

The nozzles were invented with a primary motive to change

the flow characteristics such as velocity and pressure. In

1890, Carl Gustaf Patrik de Laval developed a convergent-

divergent (CD) nozzle that had the ability to increase a steam

jet to a supersonic state [1, 2]. A typical CD nozzle and the

variation of velocity, temperature, pressure across the length

of nozzle is shown in figure 1. This nozzle was termed as a de

Laval nozzle and was later used for rocket propulsion. An

American engineer Robert Goddard was the first to integrate

a de Laval nozzle with a combustion chamber, thereby

increasing the rocket efficiency and attaining the supersonic

velocities in the region of Mach 7 [2, 3].

For space propulsion, the rocket [4, 5] is the main system

that stores its own propellant mass and ejects this mass at

high speed in order to provide thrust. A rocket engine [6–9]

generates this thrust by accelerating the exhaust gases to the

desired speed and direction. In simple words, the nozzle

utilizes the pressure generated inside the combustion

chamber to enhance the magnitude of thrust by accelerating

the combustion products to a high supersonic velocity. The

nozzle exit velocity can be controlled by the nozzle

expansion ratio or the area ratio (i.e., the exit area of nozzle

divided by the area of throat). Lesser design complexity and

weight, maximum performance, and ease of manufacture

are some of the main desirable features of a rocket nozzle.

The development of novel rocket nozzles [10] for launch

vehicles faces a challenging design problem. In order to

meet the performance of nozzle at higher altitudes, the

nozzles are designed with high area ratios. However, this

would generate over-expanded flow conditions when oper-

ated at sea level. A nozzle is said to be an over-expanded

one when its exit pressure is less than the ambient pressure.

These conditions lead to an unsteady internal flow separa-

tion resulting in the generation of side loads which may

cause damage to the whole launch system. The generation of

high magnitude side loads inside the nozzles is one of the

most important issues under consideration in designing the

reusable, robust, and efficient launch vehicles [11–13].

1.1 Brief overview

Rocket nozzles comes in a variety of configurations like

ideal, conical, bell, plug, expansion-deflection (E-D) and

dual bell besides the recently developed multi nozzle grid

(MNG). An ideal nozzle is defined as the one that produces

an isentropic flow (i.e., without internal shocks) and gives a

uniform velocity at the exit. The contour of such a nozzle

can be designed with the help of method of characteristics*For correspondence

Sådhanå (2021) 46:76 � Indian Academy of Sciences

https://doi.org/10.1007/s12046-021-01584-6Sadhana(0123456789().,-volV)FT3](0123456789().,-volV)

[14–16] (detailed in section 2). The conical type has his-

torically been the most common contour for rocket nozzles

because of its design simplicity and ease of manufacture

[16, 17]. In a conical nozzle, the exit velocity is essentially

one-dimensional (1D) corresponding to the area ratio, but

the flow is not in an axial direction across the outlet area

leading to performance loss due to flow divergence

[17, 18]. In the late 1930s and early 1940s, German sci-

entists performed extensive nozzle research [16, 19] by

considering all aspects of designing. They opined that there

was no major benefit in using contours with high com-

plexities. However, this was applicable only for low area

ratio nozzles like V-2 rocket [16, 17]. Because of its high

divergence losses, the conical type short nozzles find their

application in small thrusters and solid rocket boosters,

where simple fabrication is desired over aerodynamic per-

formance [17]. On increasing the cone angle, the thrust loss

of a conical nozzle gets enhanced due to flow divergence.

This thrust loss can be minimized by contouring the nozzle

wall and this type is referred to as the bell nozzle. This is

because, by doing this, the flow can be made to turn closer

to the axial direction [18]. Usually, the calculus of varia-

tions is the simple and direct approach for designing the

nozzle contours [14, 18]. Guderley and Hantsch [20]

investigated the problem of finding the nozzle exit area and

its contour to generate the optimum thrust for given values

of ambient pressure and nozzle length. However, the

method was not accepted widely until a simplified tech-

nique, as detailed later, was proposed by Rao [14]. In

Ariane 5 Vulcan or Space Shuttle Main Engine (SSME),

the conventional bell-type nozzle was used to expand the

propellant products [21]. On the other hand, the plug nozzle

is an altitude-compensating type rocket nozzle, where a

traditional CD nozzle expands the flow to a fixed area ratio

regardless of the freestream conditions. The free jet

boundary that acts as a virtual outer wall on a plug nozzle

expands to match the freestream ambient pressure [22, 23].

The first conceptual analysis of plug nozzles was conducted

in 1950s [21]. Though the performance benefits were

claimed in most of the literatures, however, the plug noz-

zles did not gain the hardware flight status. In the future,

this might change as the rocket engine having a linear plug

nozzle is foreseen as the propulsion system for the RLV

X-33 concept of the Lockheed Martin Corporation

[21, 24, 25]. In the E-D nozzle, the flow from the chamber

is directed radially outward and away from the axis of

nozzle. The flow is diverted towards the curved contour of

the outer diverging nozzle wall [26]. The hot gas flow

moving out of the chamber expands around a central plug.

The E-D nozzle concept had been the subject of various

experimental and analytical investigations. These studies

revealed the poor altitude-compensation capabilities of E-D

nozzle and were in fact poorer than the plug nozzles

because of over-expansion and aspiration losses. For noz-

zles with high expansion-ratio and comparatively smaller

length, an E-D nozzle performs superior than a comparable

bell nozzle of equal length. This is due to the lesser

divergence losses as compared to the bell nozzle [24]. In a

dual bell nozzle, two shortened bell type of nozzles are

joined into one with an inflection point between them. In

1949, Cowles and Foster were the first to introduce the dual

bell concept, and it was patented by Rocketdyne in 1960s

[27–29]. It is still in the conceptual stage but seems to be a

strong candidate for future rocket engines [30]. In recent

times, a newer concept of Multi Nozzle Grid (MNG) came

into the limelight where a thin and lightweight plate with

multiple small nozzles can be used instead of a lengthy and

heavy single nozzle. The saving in length is in direct pro-

portion to the square root of the number of small nozzles

(nozzlettes) in MNG (i.e., MNG with hundred nozzlettes is

ten times smaller than an equivalent single nozzle) [31–33].

1.2 Present objective

As evident from above, various shapes of rocket nozzles

have been evolved over the past 75 years, however, there is

not a single article that gives a comprehensive review of all

the types of nozzles developed till date. The present article

mainly deals with the aerodynamic features of ideal, coni-

cal, bell, plug, expansion-deflection, dual bell, and multi

nozzle grid type rocket nozzles. The review summarizes all

the facts and figures in a systematic way incorporating

several features of rocket nozzles such as design, devel-

opment, utilization, benefits and limitations along with

recommendations.

2. Ideal nozzle

When there is a parallel uniform flow with the exit pressure

matching with the ambient pressure at the nozzle exit, the

nozzle thrust becomes maximum. Such type of nozzle is

Figure 1. Variation of velocity, temperature and pressure across

the length of a De Laval nozzle [2].

76 of 22 Sådhanå (2021) 46:76

termed as an ideal nozzle. The ratio of area at exit Ae to

area at throat At of such a nozzle [18] can be expressed by

Eq. (1).

Ae

At¼ c� 1

2

� �1=22

cþ 1

� � cþ1ð Þ=2 c�1ð Þ paPc

� �� 1=cð Þ1� pa

Pc

� � c�1ð Þ=c" #�1=2

ð1Þwhere c is the isentropic exponent. The ratio pa/pc is veryless for the rocket engines working at high altitudes, and

hence more expansion ratios for the ideal nozzles is needed.

A rocket engine working over a wide range of altitudes will

give optimum performance when the nozzle expansion ratio

is variable. Because of very high temperatures involved, the

mechanical variation of expansion ratio is not easy. Thus,

an appropriate fixed expansion ratio is selected by consid-

ering the performance requirements over the complete path

of the rocket. The performance of nozzle divergent section

can be calculated (Eq. (2)) in terms of its vacuum thrust

coefficient Cfv [18] and can be expressed as:

Cfv ¼ Fv

pcAtð2Þ

where Fv is thrust when discharging to vaccum, pcand At

are the combustion chamber pressure and area of the nozzle

throat, respectively. The vacuum thrust coefficient of an

ideal nozzle is a function of isentropic exponent c and the

nozzle area expansion ratio Ae/At.

The thrust coefficient of an ideal nozzle [18] working in

an ambient pressure pa, is given by

Cf ¼ Cfvi � paPc

:Ae

Atð3Þ

The above equation is known as the 1D thrust coefficient

equation.

The uniform exit flow can be obtained when the nozzle

wall configuration is designed by the method of charac-

teristics [14–16, 34]. With the help of this method, the

system of partial differential equations can be converted to

ordinary differential equations that are valid along the

characteristic curves that represent the path of propagation

of disturbances in supersonic flows. A characteristic may be

defined as a curve along which the governing partial dif-

ferential equations reduce to an ’interior operator’s that is a

total differential equation known as the compatibility

equation. Thus, along a characteristic, the dependant vari-

ables may not be specified arbitrarily being compelled to

satisfy the compatibility equation [35–39]. High-speed

computing machines are required for the wall contour

computation. Foelsch [40–42] gave an approximation

through which the nozzle contour can be obtained by

manual computation. The length of an ideal nozzle can be

decreased by permitting all the expansion to occur just at

the throat downstream and then constructing the nozzle

contour to turn the flow such that it can attain an axial

uniform flow at the exit. To attain a uniform flow at exit,

the minimum length of the nozzle required for various

values of expansion ratio (computed for c = 1.23) is shown

in figure 2 [3]. In computing these lengths of the nozzle, it

was found that at the downstream of throat, a sharp corner

should be eluded. Hence, a wall contour of a radius of

curvature equal to 0.4 times the radius of throat was used

[18, 43]. From figure 2, it is clear that the ideal nozzle that

gives the maximum thrust performance is heavy and

lengthy. The following sections deal with the ways of

decreasing the length of nozzles without much decrement

in the performance.

3. Conical nozzle

The application of a conical nozzle was very common in

early rocket engines. The principal appeal of the conical

nozzle is that it is easy to manufacture and it has the

flexibility of converting an existing design to lower or

higher area ratio without much redesign. A typical conical

nozzle configuration is depicted in figure 3. On the basis of

length, performance and weight, the best compromised

diverging angle (a) for a conical nozzle is 15� [17, 36, 44].The thrust coefficient of a 15� conical nozzle is only 1.7%

lesser than the ideal nozzle and changes slightly with alti-

tude [18]. Thus, the performances and lengths of newer

nozzles are often compared with a 15� conical nozzle. Thelimitation of conical nozzle being heavier and longer can be

mitigated by increasing the divergent cone half-angle (a).In a conical nozzle, the performance loss takes place at a

lower altitude as higher ambient pressure leads to flow

separation and over-expansion. The major disadvantage of

conical nozzles includes the trade-off between the diver-

gence angle and the nozzle length [45].

The flow divergence in the conical nozzle leads to a

reduction in thrust as the flow direction is not completely

Figure 2. Length (calculated) comparison of several types of

nozzle (MNG: Multi Nozzle Grid, E-D: Expansion-Deflection

nozzle) [3].

Sådhanå (2021) 46:76 of 22 76

axial at the exit. Malina [46] showed that the momentum at

the exit was equal to the value calculated from 1D theory

multiplied by a correction factor, k [16, 17].

k ¼ 1þ cosa2

ð4Þ

The magnitude of correction factor, k decreases as aincreases as shown in figure 4 [46].

The conical nozzle thrust coefficient working into the

vacuum (Cfvc) is given below [18]

Cfvc ¼ pepc

:Ae

Atþ 1þ cos /

2

� �qeVe

2Ae

pcAtð5Þ

where qe, Ve, pe are the 1D density, velocity and pressure at

the nozzle exit.

Darwell and Badham [47] revealed the possibility of

shock formation within the nozzle by the method of char-

acteristics. They found that by modifying the wall contour

near the junction of the throat profile and the cone, the

shock formation could be eliminated. Khan and Shemb-

harkar [48] explained that one can capture the flow in a CD

nozzle in an overexpanded flow regime by employing a

computational fluid dynamics (CFD) code. They computed

the flow features like after-shocks, location of shocks and

lambda shocks in the CD nozzle. The centreline static

pressure plot (figure 5) for different nozzle pressure ratio

(NPR) shows that shock location moves towards the nozzle

exit as the NPR increases. Balabel et al [49] studied the

turbulent gas flow dynamics in a two-dimensional (2D) CD

nozzle and the associated physical phenomena were anal-

ysed for different operating conditions. Results showed

that, in predicting the point of separation and the position of

shock wave, the realizable v2–f and the SST (Shear StressTransport) k–x models gave better results in comparison to

other models. Hoffman and Lorenc [50] investigated 2D

gas particle flow effects in conical nozzles. Wehofer and

Moger [51] developed an analytical method to predict the

inviscid transonic flow fields linked with CD and conver-

gent conical nozzles. Jia et al [52] analysed numerically the

influence of the fire-in-the-hole staging event on the flow

separation at the start-up and side loads of a conical nozzle

during flight. Jia et al [53] further investigated numerically

the three-dimensional (3D) side loads and the associated

flow physics of a conical nozzle during the fire-in-the-hole

staging event of a multistage rocket. Zmijanovic et al [54]studied the transverse secondary gas injection into the

supersonic flow of a CD nozzle to explain the influence of

fluidic thrust vectoring within the framework of a small

satellite launcher. The results demonstrated the possibility

of attaining pertinent vector side forces with moderate

secondary to primary mass flow rate ratios ranging around

5%. They also revealed that the geometry and injector

positioning had a high influence on the nozzle performance

and shock vector control system. Figure 6 shows the

injection port and the scheme of separation alongside

nozzle wall. Zhang et al [55] performed the computational

investigation of convergent conical nozzles. The influences

of base drag and the freestream Mach number on the cal-

culated velocity coefficient were analysed. Sunley and

Ferriman [56] carried out tests to study the jet separation in

conical nozzles, and demonstrated that the pressure at

which the gas separates was neither constant nor

Figure 3. Typical configuration of a conical nozzle.

Figure 4. Variation of k with a in graphical form [46].Figure 5. Centreline static pressure (measured) plot for different

nozzle pressure ratio (NPR) [48].

76 of 22 Sådhanå (2021) 46:76

independent of the nozzle length. Migdal and Kosson [57]

studied the shock predictions in conical nozzles. Migdal

and Landis [58] investigated the performance of conical

nozzles by the application of method of characteristics.

Table 1 summarizes the various numerical, experimental

and analytical studies in the area of conical nozzles

addressing the aerodynamic aspects such as flow separation

and the shock formation.

4. Bell nozzle

The bell type nozzle is the most commonly used shape in

rocket engines. This category of nozzle provides significant

benefits in terms of performance and size over the conical

type nozzle. It has a high angle expansion section (20� to

50�) right behind the nozzle throat. This is followed by a

gradual reversal of nozzle contour slope so that at the

nozzle exit the divergence angle is small, preferably below

10� half angle. It is possible to have large divergence anglesimmediately behind the throat (20�–50�) because the high

relative pressure, the large pressure gradient, and the rapid

expansion of the working fluid that do not permit separation

in this portion unless there are discontinuities in the nozzle

contour [3]. The length of bell nozzle is generally given as

a fraction of the reference conical nozzle length. As seen in

figure 7, an 80% bell nozzle configuration that has the same

expansion ratio (e) as 15� half angle conical nozzle is 20%

smaller in length. The exit angle of 80% and 60% bell

nozzles are 8.5� and 11�, respectively [3].

A near optimum contour of the bell nozzle can be

designed by using a simple parabolic approximation pro-

cedure given by Rao [14, 59, 60]. The parabolic approxi-

mation of the bell nozzle design is shown in figure 8 [36],

where at the upstream of throat T, the nozzle contour is a

circular arc whose radius is 1.5Rt. From T to the point N,the divergent portion of the nozzle contour is made up of a

circular entrance section of radius 0.382Rt and from N to

the exit E, it is a parabola [36].

The required data for the design of a specific bell nozzle

are: diameter of throat Dt, initial wall angle of the parabola

hn, nozzle exit wall angle he, area ratio e and nozzle axial

length from throat to exit plane Ln (or the desired fractional

length Lf, based on a 15� conical nozzle) [36]. The varia-

tions of wall angles hn and he with the expansion ratio at

different values of Lf are shown in figures 9 and 10,

respectively. It is evident in figure 9 that by increasing the

expansion ratio of the bell nozzle, the value of hn increases.For a particular expansion ratio, the magnitude of hn is

larger for lower fractional nozzle length. By choosing

proper inputs, the optimum nozzle contours can be

approximated.

The thrust loss can be minimized by contouring the

nozzle wall, as by doing this, the flow can be made to turn

closer to the axial direction [18]. For contouring the nozzle

walls, various methods have been suggested in the litera-

ture. Dillaway [61] computed nozzle contours by gradually

reducing the slope of nozzle wall as one approaches

towards the nozzle exit. In a contoured nozzle, there is a

high dependency of exit flow on the nozzle contour and no

simple relation such as Eq. (5) can be derived. The

Figure 6. Scheme of the separation alongside nozzle wall [54].

Table 1. Major studies conducted on conical nozzle.

Investigators Year Nature of study Focus of study

Migdal and Landis [58] 1962 Numerical Performance of conical nozzles

Darwell and Badham [47] 1963 Numerical Shock formation

Sunley and Ferriman [56] 1964 Experimental Jet separation

Migdal and Kosson [57] 1965 Numerical Shock predictions

Hoffman and Lorenc [50] 1965 Numerical Gas-particle flow effects

Wehofer and Moger [51] 1970 Analytical Inviscid transonic flow fields

Khan and Shembharkar [48] 2008 Numerical Location of shock

Balabel et al [49] 2011 Numerical Turbulent gas flow dynamics

Zmijanovic et al [54] 2014 Experimental and Numerical Fluidic thrust vectoring

Zhang et al [55] 2015 Numerical Convergent conical nozzles

Jia et al [52] 2015 Numerical Flow separation and side loads

Jia et al [53] 2016 Numerical Side loads

Sådhanå (2021) 46:76 of 22 76

contoured nozzle vacuum thrust coefficient can be evalu-

ated as [18]

Cfv ¼Z

Ae

p

pcAt2prdr þ

ZAe

qV2coshpcAt

2prdr ð6Þ

where the integration is performed throughout the whole

area Ae of the exit plane, which is perpendicular to the axis

of nozzle. The velocity (V), direction (h) density (q), andpressure (p) are calculated at a distance r from the axis of

nozzle in the exit plane. According to Landsbaum [62], one

can analyse the various truncated ideal nozzles of different

expansion ratios and select the one which gives the best

performance [63]. Farley and Campbell [64] investigated

such truncated ideal nozzles experimentally and the results

were found to be very close to the theoretical values.

Ahlberg et al [65] presented the graphical technique for

choosing the optimum nozzle contours from a family of

truncated perfect nozzles. Rao [14] developed a method by

using the calculus of variations to design the wall contour

of the optimum thrust nozzle. For the same performance as

that of 15� conical nozzle, the length required for the bell

nozzle is shown in figure 2. Allman and Hoffman [66]

examined a technique for the design of maximum thrust

nozzle contours using direct optimization methods. The

contour of the nozzle was given by second-order

polynomial:

yðxÞ ¼ Aw þ Bwxþ Cwx2 ð7Þ

where the coefficients Aw, Bw, and Cw are determined by

mentioning the attachment angle, the exit radius and by

requiring that the polynomial contour attach continuously

to the circular-arc initial expansion contour. The authors

compared thrusts developed by the calculus of variation

contours (Rao’s method) with the thrusts generated by

polynomial contours. It was concluded that both the

methods predict essentially the same maximum thrust (i.e.,

for zero ambient pressure, the agreement was within 0.2%)

justifying the proposed technique.

Frey et al [67] presented a new nozzle contouring tech-

nique called TICTOP (figure 11), merging both Truncated

Ideal Contour (TIC) and Thrust Optimized Parabolic (TOP)

designs. The nozzle obtained is shock-free as the TIC

design and does not induce restricted shock separation

Figure 7. Comparison of a 15�conical nozzle (reference nozzle)

with 80% and 60% bell nozzles, all at an expansion ratio e of 25[3].

Figure 10. Variation of wall angles he (calculated) with the

expansion ratio e at different values of Lf (Lf = desired fractional

length (m) [36].

Figure 8. Parabolic approximation bell nozzle design configu-

ration [36].

Figure 9. Variation of wall angles hn with the expansion ratio eat different values of Lf [36].

76 of 22 Sådhanå (2021) 46:76

(RSS) which leads to high side loads. Simultaneously, it

permits a higher nozzle wall pressures at exit giving a better

margin of separation than the TOP design. Pilinski and

Nebbache [68] analysed the separated flow numerically at

various NPRs in a TIC nozzle and the pattern of a free

shock separation (FSS) was obtained for very low and high

pressure ratios. Between these two ranges of pressure

ratios, an uncommon cap shock pattern without reattach-

ment of the boundary layer appeared. Verma et al [69]

conducted tests campaign on a sub-scale TOP nozzle in

order to investigate the link between unsteady characteris-

tics of separation and reattachment shocks and the source of

side loads in rocket nozzles. Lawrence and Weynand [70]

studied the separated flow in 2D and axisymmetric nozzles

having various wall contours. Nguyen et al [71] investi-

gated the turbulent flow separation in an overexpanded

TOC nozzle. Nebbache and Pilinski [72] carried out com-

putational investigation of the flow in a TOC nozzle and

analysed the structures of flow separation at various pres-

sure ratios. Potter and Carden [73] described a method to

design the nozzles for low-density, high-speed flows with a

focus on treatment of very thick laminar boundary layers.

Baloni et al [74] performed 2D axisymmetric flow inves-

tigation within the bell type nozzle at off-design and design

conditions with the help of CFD software Fluent 6.3.26 and

GAMBIT 2.4.6. Numerical simulation was conducted

separately for two different flow conditions, i.e., hot and

cold.

Verma et al [75] carried out an experimental study to

identify the source of several flow conditions that led to the

generation of side load in a TIC nozzle. The main con-

tributors were found to be the transition in flow conditions,

i.e., the change in the circumferential shape of recirculation

portion inside the nozzle from a cylindrically dominated

regime to a conical one and the end-effect regime that

initiated a highly unsteady condition of flow in the sepa-

ration region preceding these transitions. Stark and Wagner

[76] studied the separation of boundary layer and the

related flow field in a TIC nozzle. Verma [77] performed

experiments to investigate the separation of flow in a TIC

nozzle and reported that the off-design over-expanded

nozzle flow was dominated by shock-induced boundary

layer separation that demonstrated fluctuating characteris-

tics. The separation shock fluctuates back and forth, the

magnitude of which showed a high dependence on the

contour of nozzle. Asymmetry in flow separation was also

observed at particular pressure ratios. Hagemann et al [78]tested two different types of nozzle, a thrust optimized and

a truncated ideal nozzles, for the same performance data to

explore the origin of different side loads. Results demon-

strated the highest side load in the thrust optimized nozzle

when the separation pattern changed from free to restricted

shock separation. The side load measured in the truncated

ideal nozzle was only about 33.33% of side load in the

thrust optimized nozzle. The comparison of both the nozzle

contours is shown in figure 12. Stark and Wagner [79]

performed tests to analyse the TIC nozzle flow field at low

NPR. For NPR less than 10, a convex and for NPR greater

than 20, a slight concave shaped Mach disks were found.

Terhardt et al [80] studied the side-loads and flow separa-

tion in a TIC type nozzle experimentally and analytically.

Zhang et al [12] studied numerically the aeroelastic sta-

bility for a rocket nozzle at the start-up. It was reported that

the aeroelastic behaviour of rocket nozzles were strongly

dependent upon the wall thickness and the material prop-

erties of the wall. A comparison of different nozzle con-

tours is given in table 2, while the summary of major

studies on bell nozzle is shown in table 3.

5. Plug nozzle

The plug nozzle is an advanced rocket nozzle that consists

of a primary nozzle whose shape is somewhat conventional

and a plug that helps an external expansion. The main

characteristics of this nozzle is its interaction with the

external ambient that can avoid the separation of flow

phenomena that affects a conventional bell nozzle. Such

benefits arise from the generation of expansion fan at the

primary nozzle lip and its influence on the pressure beha-

viour along the plug wall [36].

The use of plug-type nozzles has been analysed inten-

sively in recent years because of their various attractive

performance and design features. The basic concept of a

plug nozzle is not new. The manufacturers of propulsion

systems and the Lewis Research Centre of NASA have

investigated their characteristics for several years [81]. The

early turbojets of Germany installed them to attain variation

Figure 11. The TICTOP design [67]. Figure 12. Comparison of Thrust optimized contour and Trun-

cated ideal contour type nozzles [78].

Sådhanå (2021) 46:76 of 22 76

of throat area [82]. The main attraction of a plug nozzle is

that it is altitude compensating. In other words, where a

conventional CD nozzle expands the flow to a fixed area

ratio regardless of the freestream conditions, the free jet

boundary that acts as a virtual outer wall on a plug nozzle

expands to match the freestream ambient pressure. This

feature is useful for rockets used in launch vehicles, where

the NPR can range from low magnitude at launch to infinity

in the vacuum of space. The schematic of the flow field near

a plug nozzle at varying NPR is shown in figure 13 [83, 84].

At or above design NPR, the plug nozzle behaves like a

conventional CD nozzle ejecting the exhaust gases straight

back axially (at design), or, resulting in a typical under-

expanded flow condition. For NPRs lesser than the design

value, the jet boundary is pulled nearer to the plug by a

series of compression waves and expansion fans that occur

naturally in an attempt to match the ambient pressure [84].

Plug nozzles refer both to a full spike and a truncated

spike nozzles. The contoured, full-length spike nozzle is

normally referred to as a spike; while a conical, full-length

spike nozzle is defined as plug nozzle. The aerospike comes

from the idea of introducing an additional flow into the base

region of the truncated spike, forming an ‘‘aerodynamic

spike’’ with the base flow. Basically, the base flow helps fill

in the area underneath the base and supports make up for

the performance loss from truncating the nozzle [3, 36, 85].

The plug nozzle throat is situated as an annulus at the

outer diameter (not all plug nozzles utilize an annular

throat; some use engines clustered on a shared plug) with

the exhaust gases flowing in an inward direction. At the

annulus outer edge or cowl-lip, the exhaust gases expand

suddenly to the ambient pressure. The expansion waves

generating from the cowl-lip controls the flow of exhaust

gases and the flow turning is affected by the surface of the

Table 2. Comparison of various nozzle contours.

Nozzle type Key features

Conical Straight walls from throat to exit, incomplete flow turning

Truncated ideal contour (TIC) Curved walls near throat transition to nearly straight walls near the exit, virtually

complete flow turning, shortened version of the method of characteristics

Thrust optimized contour (TOC) Curved walls near throat transition to nearly straight, walls near the exit, more

sudden transition than TIC, virtually complete flow turning

Thrust optimized parabola (TOP) Parabolic approximation of TIC, higher wall pressure at exit reduces risk of side

loads

Table 3. Major studies conducted on bell nozzle.


Dillaway [61] 1957 Analytical 3D analysis of supersonic contoured nozzles

Rao [14] 1958 Analytical Method to optimize the wall contour of nozzle

Landsbaum [62] 1960 Numerical Design of bell-shaped nozzle contours

Farley and Campbell [64] 1960 Experimental Cut off portions of ideal nozzles

Ahlberg et al [65] 1961 Experimental and Numerical Optimization of truncated portions of ideal nozzles

Lawrence and Weynand [70] 1968 Experimental Separated flow in 2D and axisymmetric nozzles

having various wall contours

Potter and Carden [73] 1968 Experimental and Numerical Design of nozzles for low-density and high-speed flows

Terhardt et al [80] 2001 Experimental and Analytical Flow separation and side-loads in TIC nozzles

Verma [77] 2002 Experimental Flow separation phenomena in a TIC nozzle

Hagemann et al [78] 2002 Experimental Origin of side load in TIC and TOP

Nguyen et al [71] 2003 Experimental Turbulent flow separation in TOC nozzles

Pilinski and Nebbache [68] 2004 Numerical Separated flow in a TIC nozzle

Verma et al [69] 2006 Experimental TOP nozzle

Nebbache and Pilinski [72] 2006 Numerical Flow in an axisymmetric overexpanded TOC nozzle

Stark and Wagner [79] 2006 Experimental Analysis of flow field in a TIC nozzle at low NPR

Stark and Wagner [76] 2009 Experimental Boundary layer separation in a TIC nozzle

Frey et al [67] 2017 Numerical TIC and TOP design

Baloni et al [74] 2017 Numerical 2D axisymmetric flow analysis within the bell type nozzle

Verma et al [75] 2017 Experimental Origin of side-load generation in TIC nozzle

Zhang et al [12] 2017 Numerical Aeroelastic stability

76 of 22 Sådhanå (2021) 46:76

plug. The design of the plug surface is such that the

expansion of gases from a chamber pressure pc to an

ambient pressure pa can take place smoothly producing a

uniform flow at exit parallel to the axis of nozzle. The

external diameter of such an ideal plug is same as the exit

diameter of a uniform flow CD nozzle expanding the gases

to the same ambient pressure pa. However, the plug nozzle

is much smaller than an equivalent CD nozzle [18].

Krase [82] suggested simple approximate methods to

design ideal plug nozzle contours by manual calculations.

Berman and Crimp [81] studied the performance compar-

ison between the conventional and the plug nozzles. As

seen in figure 14, the plug nozzle shows a thrust benefit

over a conventional nozzle when it is working at below

design pressure ratio as the nature of flow in this case is

self-adjusting [81, 86, 87].

Rommel et al [21] performed computational investiga-

tion of a plug nozzle and gave an understanding of the

development of flow field at various ambient pressures.

Figure 15 shows a typical conventional nozzle, a truncated

and a full length plug nozzle. Ito et al [88] investigated the

flow fields of a plug nozzle with the help of a numerical

simulation. They designed the plug contour by the method

of characteristics and various types of plug nozzles were

considered by truncating the nozzle length at various

positions. Results showed an increase of thrust performance

of the contoured plug nozzle by about 5 to 6% than the

conical plug nozzle, and the pressure distribution on the

nozzle surface was unaffected by the external flow for the

pressure ratios more than the designed point. Chutkey et al[89] analysed the flow fields associated with truncated

annular plug nozzles of varying lengths. On the other hand,

Shahrokhi and Noori [90] studied the flow properties of

various aerospike nozzle shapes. They used the k-e turbu-

lence model and Navier-Stokes equations for the simulation

of flow field. A uniform cubic B-spline curve was used to

generate the various plug shapes, and the best configuration

was determined by considering the total thrust force as a

performance merit. Kumar et al [91] discussed the proce-

dure to design a plug nozzle and the parameters governing

its design. Johnson et al [92] presented an optimization

analysis for plug nozzles with variable inlet geometry.

Besnard et al [93] presented the design, manufacturing and

tests of a 1000 lbf thrust ablative annular aerospike engine.

Results showed that variations in c with temperature led to

small, albeit not null, differences in thrust and plume

characteristics. Further, the nozzle was found to be very

efficient. Lahouti and Tolouei [94] carried out numerical

modelling of external and internal flows of a truncated plug

nozzle with several amounts of base bleed in under-ex-

pansion, optimum and over-expansion working conditions

Figure 13. Flow field of a plug nozzle with full length at different pressure ratios pc/pa, off-design [pc/pa\ (pc/pa)design] left, [pc/pa[(pc/pa)design] right and design pressure ratio (centre) [83, 84].

Figure 14. Comparison of theoretical performances (calculated)

of conventional and plug nozzles [81, 86, 87].

Figure 15. Typical (a) conventional nozzle, (b) truncated nozzle

and (c) full length plug nozzle [21].

Sådhanå (2021) 46:76 of 22 76

to obtain the nozzle’s base thrust, base pressure distribution

and flow pattern. A variation of the non-dimensional total

base thrust (CFbase) with the pressure ratio (pa/pdes) for

different amount of base bleed is shown in figure 16.

Shanmuganathan et al [95] carried out the study of linear,

annular aerospike nozzles and the characteristics of its flow

field. They opined that the annular aerospike nozzle was

better than the linear aerospike nozzle.

The central plug body truncation is beneficial because it

eliminates the huge ideal length and heavy structural mass

of the well contoured body, and this truncation results in a

different flow and performance behaviour as compared to

the full length plug [3, 96]. At lesser pressure ratios, an open

wake flow is established with a pressure level equal to the

ambient pressure. At a certain pressure ratio close to the

design pressure ratio of the full length plug nozzle, the base

flow suddenly changes its character and turns over to the

closed form, characterized by a constant base pressure that

is no longer affected by the ambient pressure. Analyses

indicated that smaller plug bodies with higher truncations

leads to an earlier change in wake flow at pressure ratios

below the design pressure ratio [24]. At the point of tran-

sition, the pressure inside the wake reaches below the

ambient pressure, and the full base area generates a negative

thrust. This loss of thrust depends on the percentage of

truncation and the total size of the base area. The results

demonstrated an increase in the thrust loss for smaller plug

bodies as the total base area increases. Beyond the pressure

ratio at transition, the pressure inside the closed wake

remains constant. A further decrease of the ambient pressure

leads to a positive thrust contribution of the total base area

[24, 83]. An experimental investigation by Ruf and

McConnaughey [97] stated that a 50% truncation of the plug

nozzle resulted in only a 0.5% reduction in its performance.

In order to avoid a flat base at the vertex of plug after the

truncation, a larger cone angle could be used at the plug end.

Berman and Crimp [81] showed the performance decrement

of only 1% by using cone half angles, even up to 30� at the

plug end. The approach that is used to optimize the contour

of conventional nozzles can also be used to optimize the

plug contour. The solution of such problems was discussed

by Rao [98], where he presented typical optimum plug

contours. By the use of a plug, the reduction in length of the

nozzle can be obtained as indicated in figure 15.

As compared to other types, the major disadvantage of a

plug nozzle lies with its high cooling requirements because

of higher heat fluxes and greater surface areas to be cooled

[21, 36]. The central plug of a spike nozzle if heated to

higher values (greater than the material limitations) would

require a secondary cooling system to be installed to cool

the plug and prevent failures. Overcoming this problem

using secondary active cooling system greatly affects the

mass of vehicle. The summary of major numerical and

experimental studies of plug nozzles is shown in table 4. In

case of plug nozzles, the key areas that have drawn atten-

tion to the researchers are the optimization of the nozzles’

contour and their truncation.

6. Expansion-deflection nozzle

The expansion-deflection (E-D) nozzle is an altitude com-

pensating type rocket nozzle where the altitude compen-

sation is attained through the interaction of exhaust gas

with the atmosphere. It looks similar to a bell nozzle, but a

’pintle’ or ’centre body’ is placed at the throat and because

of that the flow is diverted towards the wall [26]. The

benefit with the centre body is that it makes the exhaust gas

to flow in a more outward direction than in bell nozzles.

Due to this, the size of the nozzle decreases considerably as

compared to the conventional nozzles of the same expan-

sion ratio. This nozzle works in closed and open wake

modes. In closed wake mode, the entire exit area of nozzle

is filled by the exhaust gases. The ambient pressure at

which the transition of wake takes place from open to

closed modes is known as the design pressure. If the

ambient pressure is further decreased, then the remaining

expansion would occur outside the nozzle just like a bell

nozzle and in that case there is no benefit of altitude

compensation. In open wake mode, the ambient pressure

controls the exit area of nozzle and the exhaust gas does not

fill the complete nozzle. As the area ratio is controlled by

the ambient pressure, the altitude compensation is achieved

up to the design pressure [99, 100].

When there is a high chamber to ambient pressure ratio

(pc/pa), the performance of the E-D nozzle is similar to that

of a plug nozzle [18]. However, when the pressure ratio is

lesser, the flow in a plug nozzle adjusts itself to the pressure

at the cowl-lip. On the other hand, in an E-D nozzle, the

flow adjusts itself to the pressure occurring behind the

central plug. The combustion chamber of the E-D nozzle is

small in size, and it has thus some benefits regarding

cooling requirements and weight. When a nozzle with veryFigure 16. Variation of total base thrust (calculated) with

ambient pressure for different base bleeds [94].

76 of 22 Sådhanå (2021) 46:76

high expansion ratio is required, the best choice is an E-D

nozzle because of its compact sized combustion chamber

and smaller length [18]. Rao [101] studied the flow between

the walls of the combustion chamber and the plug by using

a series expansion and described the method of designing

the optimum nozzle wall contour. Results showed that for

the same performance as that of bell nozzle, the length of

an E-D nozzle required was only 50% to that of bell nozzle

length. The variation of the various nozzles thrust coeffi-

cient with the altitude is shown in figure 17 [101].

Schomberg et al [100] studied the dependency of thrust

coefficient on the E-D nozzle geometry when the flow

conditions were highly over-expanded. Results show that

the nozzle thrust depends upon the rate of change of area

through the transonic region and the linear E-D type nozzle

has shown a higher thrust as compared to conventional

nozzle when the flow conditions are highly over-expanded.The flow behaviour in open and closed modes in the E-D

nozzle is shown in figure 18 [100]. Schomberg and Olsen

[102] designed and tested the E-D nozzle at different

pressure ratios to represent operation over a range of the-

oretical altitudes (figures 19 and 20). They reported the

efficiency of E-D nozzle to be more than the conventional

CD nozzle. Wasko [103] studied the performance of plug

and E-D nozzles where the influence of base bleed were

also analysed. Results showed that the performance of full

length plug nozzle was better, whereas the performance of

the E-D nozzle was only comparable to that of a conical CD

nozzle. Schomberg et al [26] compared the linear variant of

an E-D nozzle to a conventional CD nozzle through an

experimental investigation, and demonstrated that the thrust

coefficient in the E-D type nozzle was 25–100% more than

the CD nozzle across the tested range of pressure ratios.

Schomberg et al [104] carried out numerical analysis of

E-D and CD nozzles. Results were noted over a range of

theoretical altitude and were compared to experimental

static pressure readings and schlieren images. The corre-

lation between experimental and numerical static pressure

values were found to be high for all operating conditions.

Currao et al [105] reported the use of Pressure-Sensitive

Paint (PSP) and infrared camera to a small linear asym-

metric nozzle. Their project aimed to validate numerical

results through the PSP measurements. Taylor et al [106]studied the evacuation effect in E-D nozzles. Mueller and

Hall [107] analysed the region of separated flow within a

E-D type nozzle. Taylor and Hempsell [108] carried out the

optimization of E-D nozzles for vacuum thrust. The major

experimental and numerical studies in the area of E-D

nozzles are summarized in table 5. In most of the cases,

they are related to the design of optimum wall contour of

nozzle, flow separation, and evacuation effects.

Table 4. Major studies conducted on plug nozzle.


Krase [82] 1959 Numerical Design of ideal plug nozzle contours

Berman and Crimp [81] 1961 Analytical Modification of plug end

Rao [98] 1961 Numerical Optimization of plug contours

Johnson et al [92] 1974 Numerical Optimization for axisymmetric plug nozzles

Rommel et al [21] 1997 Numerical Flow field development at different ambient pressures

Ruf and McConnaughey [97] 1997 Numerical Truncation of plug nozzle

Ito et al [88] 2002 Numerical Designing of plug contour

Besnard et al [93] 2002 Experimental Design and testing of thrust ablative annular aerospike engine

Lahouti and Tolouei [94] 2006 Numerical External and internal flows of a truncated plug nozzle with base bleeds

Shahrokhi and Noori [90] 2010 Numerical Flow properties of aerospike nozzle shapes

Chutkey et al [89] 2014 Numerical

and Experimental

Flow fields in truncated annular plug nozzles of varying lengths

Shanmuganathan et al [95] 2015 Numerical Flow field study of linear and annular aerospike nozzles

Kumar et al [91] 2017 Numerical

and Experimental

Design procedure of aerospike nozzle

Figure 17. Variation of various nozzles thrust Performance

(calculated) with altitude (E-D: Expansion-Deflection nozzle)

[101].

Sådhanå (2021) 46:76 of 22 76

7. Dual bell nozzle

Dual bell nozzles have been seen as a solution to maximize

the efficiency at high altitudes while eluding hazardous side

loads at lower altitudes. As can be seen in figure 21, a dual

bell nozzle consists of two different contours as opposed to

one between the throat and exit. It is composed of a base

contour that is separated from the extension contour by an

inflection in the wall. [110, 111]

In 1949, Cowles and Foster first introduced the concept

of a dual bell nozzle, and the design was patented by

Rocketdyne in the 1960s [27–29]. As the CFD capabilities

developed with time, the research activities gained attention

in the 1990s. The confirmation of the feasibility of this

nozzle was done by Horn and Fisher [27] by conducting

tests at Rocketdyne and in Europe by the Future European

Space Transportation Investigations Programme (FESTIP)

at the European Space Agency (ESA) [27]. They investi-

gated four contour combinations to find the extension

contour that provided the most favourable flow transition

characteristics and high altitude performance as compared

to the performance of two baseline contours. The perfor-

mance of the dual bell nozzles was demonstrated to be

lesser than the theoretical optimum because of the losses

linked with aspiration drag during low-altitude mode and

non-optimum contour in high-altitude mode. Horn and

Fisher found that even with such losses, a dual bell nozzle

could deliver sufficient thrust to carry 12.1% additional

payload as compared to a conventional CD nozzle having

the identical expansion ratio. The first numerical analysis of

dual bell nozzles was done by Goel and Jensen, which was

published in 1995 [112]. Throughout the 2000s, in Europe

and in the United States, various experimental and

numerical investigations of dual bell nozzles were per-

formed [24]. Modern studies focus on optimizing particular

design variables of the dual bell nozzle such as the ideal

contour and relative length of the extended section.

With the help of nozzle wall inflection, this nozzle gives

an altitude adaptation. Controlled and symmetrical sepa-

ration of flow takes place at this wall inflection at low

altitudes which leads to a less effective expansion ratio. The

flow in the nozzle is attached to wall at higher altitudes

until the full geometrical expansion ratio is utilized. An

improved vacuum performance is attained due to the higher

expansion ratio [110, 113]. However, some additional

performance losses are induced in dual bell nozzles. The

main benefits of this nozzle lie with the control of flow

Figure 18. E-D nozzle flow behaviour in a open mode and b closed mode [109].

Figure 19. Pressure distribution at a 450 kPa inlet [102].

Figure 20. Pressure distribution at a 550 kPa inlet [102].

76 of 22 Sådhanå (2021) 46:76

separation and its design simplicity. While other altitude

compensating nozzle concepts have the limitations of

mechanical complexity, cooling difficulty, and more weight

and price tag. The dual bell nozzle provides an exceptional

blend of simplicity, lesser weight, performance and ease of

cooling [24].

Kbab et al [114] designed the profile of a dual bell nozzleand studied the flow behaviour using the method of char-

acteristics. Genin et al [115] conducted experimental and

numerical studies on a dual bell nozzle for the evaluation of

heat flux distribution. For both the operation modes (sea

level and altitude), the heat flux value was found to increase

in the region of the contour inflection. The heat flux value

increased by about 40% in altitude mode. In sea level mode

and during the sneak transition, the flow separation in the

region of the inflection increases this phenomenon. The two

operation modes of a dual bell nozzle are depicted in fig-

ure 22. Under sea level conditions, the flow separates at the

contour inflection in a controlled and symmetrical way

(figure 22a). The generation of side load is continued to

decrease and the thrust enhances due to the small area ratio.

During flight, the ambient pressure reduces, which results

in an increase in the NPR. At a particular height, the

transition NPR is reached and the separation point leaves

the contour inflection and moves rapidly to the nozzle exit.

The extension then flows full (figure 22b). The thrust is

enhanced due to the greater area ratio.

The variation of specific impulse with altitude for a dual

bell and two conventional nozzles is shown in figure 23

[115]. Schneider and Genin [116] analysed the effect of

various turbulence models and feeding pressure gradients

on the dual bell flow transition behaviour. They found

improved results for the Reynolds stress turbulence and

Spalart–Allmaras model. Genin et al [117] tested a planar

dual bell nozzle model under several test conditions in cold

and hot flows. The analysis of the shock in the region of the

contour inflection gave an idea of the shape and position of

the separation front. In sea level mode, the numerical and

experimental results were in good agreement; and for

higher NPR values, the calculated separation position was

situated further upstream than measured in the experiments.

Table 5. Major studies conducted on E-D nozzle.


Rao [101] 1960 Numerical

and Experimental

Method of designing nozzle wall contour to yield optimum thrust

Mueller and Hall [107] 1968 Experimental Region of separated flow

Wasko [103] 1968 Experimental Effects of base bleed

Taylor and Hempsell [108] 2004 Numerical Optimization of E-D nozzles for vacuum thrust

Taylor et al [106] 2010 Experimental Analysis of the evacuation effect in E-D nozzles

Schomberg and Olsen [102] 2012 Experimental Designing and testing of E-D nozzles at different pressure ratios

Schomberg et al [100] 2014 Numerical

and Experimental

Effect of E-D nozzle geometry on calculated thrust coefficient

Schomberg et al [26] 2014 Experimental Comparison of linear variant of the E-D nozzle to a conventional

CD nozzle

Schomberg et al [104] 2014 Numerical Analysis of annular CD and E-D nozzles

Currao et al [105] 2014 Experimental Application of PSP and Infrared camera to a small linear asymmetric

nozzle

Figure 21. A typical dual bell nozzle.

Figure 22. Two operation modes of dual bell nozzle: a sea level

and b altitude mode [115].

Sådhanå (2021) 46:76 of 22 76

Stark and Genin [118] studied the characteristics of side

load in a dual bell nozzle. Verma et al [119] did experi-

mental investigation to study the Reynolds number effect

on transition behaviour of dual bell nozzle for tests inside a

high altitude simulation chamber. Verma et al [120] furtherconducted experiments to investigate the dependency of

transition behaviour on ambient pressure fluctuations in

dual bell nozzle. Toufik et al [121] studied the design of

dual bell nozzles and evaluated several wall parameters and

performances with the help of the method of characteristics.

Davis et al [28] developed the design procedure of dual bell

nozzle contour and used it to analyse the nozzle that could

be installed on a nanosatellite launcher or a sounding

rocket. Verma et al [111] studied the unsteady flow con-

ditions occurred during sneak transition by conducting

cold-gas test on a subscale dual bell nozzle working under

sea level conditions. The results showed that the flow

during sneak transition was highly unsteady and was the

major source of side load generation. Genin et al [122]

performed the numerical and experimental studies to opti-

mize the transitional behaviour through the variation in

extension geometry. Hagemann et al [123] had done the

analytical and experimental work to explore the aerody-

namic characteristics of various dual bell nozzles. Frey and

Hagemann [112] investigated various aspects of design for

the wall inflection and nozzle extension with focus on the

dependency of transition behaviour on the type of nozzle

extension. Results showed that two different types of noz-

zle extensions (overturned and constant pressure) might

offer the sudden flow transition. Genin et al [124] investi-gated computationally the flow behaviour in a dual bell

nozzle and analysed the two operation modes and the

transition from one mode to the other by changing the NPR.

Table 6 summarizes the experimental, analytical and

numerical studies of the dual bell nozzles.

7.1 Extendable nozzles

Extendible nozzles were used as a substitute to dual bell

nozzles earlier. This nozzle is commonly known as an

extendible exit cone (EEC). It has a fixed low-area-ratio

section, which is enlarged to a higher area ratio by attaching

one or more nozzle cone extension parts. The specific

impulse of such nozzles increases by doubling or tripling

the initial area ratio. This configuration permits very high

area ratio nozzles to be bundled in a relatively short length

that helps in decreasing vehicle inert mass. [125]

8. Multi nozzle grid

The Multi-Disciplinary Optimization (MDO) procedure

[31] creates a thin and lightweight Multi Nozzle Grid

(MNG) plate (figure 24) instead of a lengthy and heavy

single nozzle. The length saving is in direct proportion to

the square root of the number of small nozzles (nozzlettes)

in the MNG (i.e., MNG with hundred nozzlettes is ten times

smaller than an equivalent single nozzle) [31–33]. Past

study reveals the overall improvement in performance via

mass saving and nozzle efficiency. The mass saving results

in substantial improvement of structural mass ratio, while

improvement in nozzle efficiency is attained by using

strategies that minimize thermodynamic losses yet increase

area ratio. Since the beginning of rocketry, the nozzle

designers mainly focused on how to increase the perfor-

mance of a nozzle without enhancing its weight and length.

The same task is just as important today with the devel-

opment of advanced materials. MNG is the only nozzle

configuration where the nozzle length (i.e., plate thickness)

to throat diameter can be less than one, yet is capable of

providing extremely high area ratio [31]. Chasman et al[31] have studied the MDO to design an innovative multi-

nozzle configuration. Later on, Chasman et al [32] have

carried out the hot-fire tests of 91 nozzlettes MNG con-

figuration characterized by exceedingly high nozzle erosion

at an average rate of 0.5 lb./sec. The high erosion of copper

infiltrated tungsten, traditionally considered being ‘‘a well-

defined refractory material’’ underlines the need to match

the structural material of the nozzle with the environment

of propellant by-products. Material experts are in the

opinion that the excessive erosion observed, occurred due

to the sensitivity of tungsten to flow of hot carbon

monoxide through the nozzlettes. Such sensitivity is inde-

pendent of nozzle configuration and would also prevail in

conventional single nozzle. Chasman et al [33] further

studied the viscous losses of MNG in hybrid motor tests.

The viscous losses in the flow through the MNG dropped

the efficiency by 3% as compared to that of an Equivalent

Single Nozzle (ESN). It can be mentioned here that a single

nozzle that shares the same scaled nozzle contour and

overall throat area as well as exit area is called an ESN. But

when compared to a conventional single nozzle (CSN) thatFigure 23. Variation of specific impulse with altitude for a dual

bell and two conventional nozzles [115].

76 of 22 Sådhanå (2021) 46:76

are commonly used in air vehicles, the MNG system may

improve the performance by more than 11% because of its

mass and length savings. The major experimental studies in

the area of MNG are shown in table 7.

In summary, a list of rocket engines stating their appli-

cations and the type of nozzles used along with their cor-

responding nozzle area ratio are shown in table 8, while the

characteristics of all the rocket nozzles starting from the

ideal to the MNG types are shown in table 9.

The performance comparison of various nozzles is

shown in figure 25. The nozzle thrust coefficient, CF for an

ideal nozzle (in this figure, the ideal nozzle refers to a

variable area-ratio nozzle having the optimum expansion

for each chamber pressure to ambient pressure ratio, pc/pa)is shown together with those of the high area-ratio aero-

dynamic spike and bell nozzles. As is evident, the CF curve

of the aerodynamic spike follows the ideal nozzle perfor-

mance (altitude-compensation), rather than dropping off

rapidly like the bell design at low pc/pa (i.e., sea level)

operating points. All the nozzles have a higher CF at a high

pc/pa (i.e., vacuum).

9. Losses in rocket nozzles

The two important losses encountered in rocket nozzles are

summarized below:

Table 6. Major studies conducted on dual bell nozzle.


Horn and Fisher [27] 1994 Experimental Performance characteristics of dual bell nozzles

Frey and Hagemann [112] 1999 Analytical

and Experimental

Dependence of the transition behaviour on

the type of nozzle extension

Hagemann et al [123] 2002 Analytical

and Experimental

Aerodynamic characteristics

Stark and Genin [118] 2010 Experimental Characteristics of side load

Genin et al [124] 2012 Numerical Flow behaviour in a dual bell nozzle

Genin et al [122] 2013 Numerical

and Experimental

Optimization of the transitional behaviour through variation

of extension geometry


and Experimental

Determination of heat flux distribution.


and Experimental

Planar dual bell nozzle under several test conditions

Verma et al [119] 2013 Experimental Reynolds number influence on dual bell transition behaviour

Verma et al [120] 2014 Experimental Influence of ambient pressure fluctuations on the dual bell transition

behaviour

Davis et al [28] 2015 Numerical

and Experimental

Dual bell nozzle contour design procedure

Verma et al [111] 2015 Experimental Unsteady flow conditions encountered during sneak transition

Schneider and Genin [116] 2016 Numerical Effect of various turbulence models and feeding pressure gradients on

dual bell flow transition behaviour

Toufik et al [121] 2016 Numerical Design of dual bell nozzle

Kbab et al [114] 2017 Numerical Design of dual bell nozzle profile

Figure 24. Schematic of Multi Nozzle Grid (MNG) [31].

Table 7. Major studies conducted on Multi Nozzle Grid (MNG).


Chasman et al [31] 2005 Experimental MDO method for MNG design

Chasman et al [32] 2005 Experimental Nozzle erosion in a MNG

Chasman et al [33] 2012 Experimental Viscous losses of MNG in hybrid motor tests

Sådhanå (2021) 46:76 of 22 76

Table 8. Key features of few rocket engines used in the past [43].

Rocket engines Application Nozzle used Nozzle area ratio

RS-1801 Lunar excursion module ascent engine 72% Bell 45.6

AJ10-138 Titan III transtage Bell 40

YLR99-RM-1 X15 Aircraft; Pioneer spacecraft Conical 9.8

YLR113-AJ-1 Rocket sled Conical 5.7

RL10A-3-3 Centaur upper stage Bell 57

AJ10-137 Apollo service module Bell 62.5

LR91-AJ-5 Titan II stage Bell 49.2

LR89-NA-7 Atlas MA-5 Booster engine 100% Bell 8

J-2 S-II and S-IV stages of Saturn V Bell 27.5

F-1 S-1C stage of Saturn V Bell 16

Model 8093 Centaur ACS and ullage orientation Conical 15

M2A Comsat positioning and orientation Conical 40

SE-7 Gemini attitude control 80% Bell (Scarfed) 40.2

PD6000179 Titan III transtage ACS Optimized Bell 49

SE-7-1 Saturn SIV-B ullage 80% Bell (Scarfed) 40

Table 9. Characteristics of various rocket nozzles.

Types of nozzle Characteristics

Ideal Give maximum thrust performance

Long and heavy

Conical Easier manufacturing

Easier optimization

Flow at exit is not completely axial

Requires a trade-off between divergence angle and nozzle length

Pressure thrust is not optimum at all altitudes

Bell Lesser length as compared to conical nozzle

Performance is higher as compared to conical nozzle

Manufacturing is difficult

Pressure thrust is not optimum at all altitudes

Optimization is difficult

Plug Flow separation can be avoided

Allow near optimum expansion at all altitudesu

Less noisy

Lesser size as compared to conventional nozzle

Cooling of central plug is difficult

E-D Allow near optimum expansion at all altitudes

Size is lesser as compared to conventional nozzle

Easier cooling

Combustion chamber is compact

Performance is low as compared to plug nozzle

Higher throat heat fluxes relative to a conventional bell nozzle with an

equal throat area

Dual bell Can carry more payload as compared to conventional nozzles

Controlled flow separation

Easier cooling

Higher performance and reliability

Difficult to optimize the wall contour

Lesser side loads

Lower weight

Difficult to manufacture

MNG Better performance as compared to other types of nozzles

Lesser length

76 of 22 Sådhanå (2021) 46:76

9.1 Two-phase flow loss

Solid rocket motors (SRMs) carrying evenly mixed ener-

getic solid propellants have several benefits such as high

reliability, structural simplicity, and ease of maintenance.

Hence, such SRMs are extensively used as boosters for

spacecraft/launch vehicles. However, the co-existence of

high-energy metal additives and the oxides generated in the

chamber during the working process may lead to loss of

two-phase flow resulting in poor performance of the SRMs.

9.2 Impingement Loss

The impingement of a thruster exhaust plume on spacecraft

structures lead to loss of thrust depending on the configu-

ration of the surfaces affected. Mitigating the effects of the

interaction between rocket exhaust plumes and neighboring

structures is a perpetual problem in the spacecraft propul-

sion system design. The plume shear against the interior

cylindrical surface results in an effective thrust loss, while

the plume impingement against the cylinder base generally

has a negligible effect on the net axial thrust. [3, 127]

10. Thrust vector control in rocket nozzles

Rocket propulsion systems deliver a push in the direction of

desired end point, but such systems can also provide tor-

ques in order to rotate the vehicle in conjunction with the

propulsive force. The thrust vectors direction can be con-

trolled using the mechanisms described below. These

mechanisms can influence a vehicle’s yaw, pitch, and roll

rotations. [128–131]. The thrust vector control mechanisms

can be divided into four groups:

a. Mechanical deflection of the main nozzle or thrust

chamber [128].

b. Insertion of heat-resistant movable bodies into the

exhaust jet; these experience aerodynamic forces and

cause deflection of part(s) of the exhaust gas flow [129].

c. Injection of fluid into a side portion of the diverging

nozzle section causing an asymmetrical distortion of the

supersonic exhaust flow [130].

d. Separate thrust-producing unit that is not a part of the

main propulsion system providing flow through one or

more of its own nozzles [131].

11. Conclusion and recommendation

Rocket nozzle designers are always being challenged to

search for the resolution to use a smaller size nozzle in

harvesting a higher specific impulse while maximizing the

cost saving and simplifying the structural complexity.

Lesser weight, maximum performance, and ease of manu-

facture are some of the main desirable features of a rocket

nozzle. This review paper attempts to analyse the major

research work done in the area of rocket nozzles during the

last 75 years. Some of the salient points from the present

review work are summarized below.

• The thrust of a rocket nozzle becomes optimum when

there is a parallel uniform flow at the exit and having

the exit pressure equal to the ambient pressure, but this

makes the nozzle longer and heavier.

• A conical nozzle is easier to manufacture and has the

flexibility of converting the existing design to lower or

higher area ratio without much redesign. The thrust

coefficient of a 15� conical nozzle is only 1.7% lesser

than the ideal nozzle.

• The shock formation in a conical nozzle can be

eliminated by modifying the wall contour near the

junction of throat profile and cone. The numerical

results show that the realizable v2–f and the SST k–xmodels give better results as compared to other models

in predicting the position of separation point and the

shock wave in the conical nozzle. The major disad-

vantage lies with the trade-off between the divergence

angle and the nozzle length.

• Bell type nozzle is the most commonly used shape in

rocket engines. This type of nozzle offers significant

benefits in terms of size and performance over the

conical nozzle. The thrust loss experienced in a conical

nozzle due to the flow divergence can be decreased to

some extent by the bell nozzle. The side load measured

in the truncated ideal nozzle is about 33.33% of side

load in the thrust optimized nozzle. The use of the

parabolic approximation procedures seems to be the

easier method to optimize the bell nozzle contour.

• The length of a plug nozzle is significantly lesser than

an equivalent CD nozzle. These types of nozzles are

meant for altitude compensating. The main property of

a plug nozzle is its interaction with the external

ambient that is capable to eliminate the flow separa-

tion. Plug nozzle shows a thrust benefit over a

Figure 25. Nozzle performance comparison (calculated) [126].

Sådhanå (2021) 46:76 of 22 76

conventional CD nozzle when it is working below

design pressure ratio. The thrust performance of a

contoured plug nozzle is around 5–6% more than the

conical plug nozzle. A 50% truncation in plug nozzle

results in only a 0.5% loss in its performance. The

major disadvantage of such nozzles lies with its

relatively high cooling requirements.

• The length of an E-D nozzle is approximately the same

to that of a plug nozzle for an equivalent thrust

performance. For the same performance as that of a

bell nozzle, the length of an E-D nozzle required is

only 50% to that of a bell nozzle. The thrust coefficient

of an E-D nozzle is 25-100% more than the CD nozzle.

As the combustion chamber of a rocket engine with an

E-D nozzle is compact in size, it has certain benefits

regarding cooling requirements and weight. When

there is a need of a very high expansion ratio, the best

choice is the E-D type nozzle.

• Dual bell nozzles have the advantage of maximum

efficiency at high altitudes while no side loads at low

altitudes. This nozzle provides sufficient thrust to carry

12.1% more payload as compared to a conventional

CD nozzle having the same expansion ratio. The main

benefits of a dual bell nozzle are its ability to control

flow separation, besides its design simplicity and high

reliability. The heat flux value in a dual bell nozzle

increases in the region of the contour inflection for

both the operation modes. The flow during sneak

transition is highly unsteady and is the major origin of

side-load generation in the dual bell nozzle preceding

the final transition. Other altitude compensating noz-

zles have the limitations of mechanical complexity,

cooling difficulty, and more weight and price tag. The

dual bell nozzle provides an exceptional amalgam of

performance, simplicity, lesser weight, and ease of

cooling.

• In MNG, the length saving is in direct proportion to the

square root of the number of nozzlettes. This is the

only nozzle configuration where the nozzle length (i.e.,

plate thickness) to throat diameter can be less than one,

yet is capable of providing extremely high area ratio.

Viscous losses in the MNG drop the efficiency by 3%

as compared to that of the ESN. However, as compared

to a CSN, the MNG system may improve the

performance by more than 11% because of mass and

length savings.

As evident from the above comprehensive literature

review, each design has its specific strengths and weak-

nesses, and there is no design that stands out as clearly

superior to the others. Rather, the selection of a particular

design results from a careful trade-off between different

factors such as application, performance, reliability,

mechanical complexity, manufacturability, weight, and

cost. The ‘winning’ concept from such a trade-off is further

influenced by how these factors are ranked in order of

importance. Based on the results presented in this review

and a look at which designs have received greatest attention

till date, the dual bell and MNG nozzles seems to be the

two most attractive candidates; the dual bell nozzle because

of its simplicity, and the MNG nozzle due to its lesser

length.

Acknowledgements

The authors wish to place on record their sincere gratitude

to all the authors of classical and popular papers/reports/

theses which formed the framework of the present review

work. Appreciation is extended to all the sources of

figures and data used in this work. A list of these sources

has been included in the references, and the authors

apologize if due recognition to any source is left out

inadvertently.

List of symbolsAe Nozzle exit area (m2)

At Throat area (m2)

Cfv Vacuum thrust coefficient

Cfvc Conical nozzle vacuum thrust coefficient

Cfvi Ideal nozzle vaccum thrust coefficient

CFbase Total base thrust

CF Thrust coefficient

CF,X Axial thrust coefficient

CFi Ideal thrust coefficient

Dt Throat diameter (m)

Fv Thrust when discharging to vaccum

HN Nozzle projected height (m)

Isp Specific impulse (sec)

L Nozzle length (m)

Ln Nozzle axial length from throat to exit plane (m)

LN Nozzle projected length (m)

Lf Desired fractional length (m)

pa Ambient pressure (Pa)

pc Chamber pressure (Pa)

pdes Design pressure (Pa)

pe Pressure at the exit (Pa)

pt Stagnation pressure (Pa)

pw Wall pressure (Pa)

R Radius of circular arc (m)

Rt Throat radius (m)

Ve Nozzle exit velocity (m/s

Greek symbolsa Divergent cone half-angle (deg.)

qe Density at the exit of nozzle (kg/m3)

c Isentropic exponent

e Nozzle expansion ratio or area ratio

h Nozzle convergent cone section half-angle (deg.)

he Nozzle exit wall angle (deg.)

hn Initial wall angle of the parabola (deg.)

76 of 22 Sådhanå (2021) 46:76

AbbreviationsAR Area ratio

CD Converging-diverging

CFD Computational fluid dynamics

CSN Conventional single nozzle

E-D Expansion-deflection

EEC Extendable exit cone

ESA European space agency

ESN Equivalent single nozzle

FESTIP Future European space transportation

investigations programme

FSS Free shock separation

MDO Multi-disciplinary optimization

MNG Multi nozzle grid

MOC Method of characteristics

NASA National aeronautics and space administration

NPR Nozzle pressure ratio

PSP Pressure-sensitive paint

RSS Restricted shock separation

SRM Solid rocket motor

SSME Space shuttle main engine

SST Shear stress transport

TIC Truncated ideal contour

TOC Thrust optimized contour

TOP Thrust optimized parabola

1D One dimensional

2D Two dimensional

3D Three dimensional

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Rocket nozzles: 75 years of research and development

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